Methodology for expressing the flow coefficients of coupled throttling grooves in a proportional–directional valve

Calculating the flow coefficient of a spool-valve is complicated due to the coupling–throttling effect in the throttling grooves of a proportional–directional valve.In this paper,a methodology for expressing the flow coefficient of coupled throttling grooves is proposed to resolve that difficulty.With this purpose,an approach of a 3 D numerical simulation and an experimental bench were introduced based on the prototype of a commercial proportional valve.The results show consistency between the numerical simulation and the bench test.Based on that,the concept of‘saturation limit’is introduced to describe the value gap between the current and saturated flows,so that the flow-coefficient saturation limit of the prototype in the process can be deducted.Accordingly,an approximate flow coefficient suitable for coupled throttling grooves within finite variable space,which is based on three typical throttling structures(i.e.O-shape,U-shape,and C-shape)of the coupled throttling grooves,is obtained based on an orthogonal test.The model results are consistent with the numerical and experimental results,with maximum errors of less than 5.29%and 5.34%,respectively.This suggests that the proposed method is effective in approximating the flow coefficient.